On the Helmholtz conditions for the existence of a Lagrange formalism

1975 ◽  
Vol 26 (2) ◽  
pp. 481-492 ◽  
Author(s):  
E. Engels
Keyword(s):  
Helmholtz Conditions ◽  
Lagrange Formalism

On the Euler-Lagrange formalism to compute power line bundle conductors subject to aeolian vibrations

2022 ◽  
Vol 163 ◽  
pp. 108099
Author(s):  
Y.D. Kubelwa ◽  
A.G. Swanson ◽  
K.O. Papailiou ◽  
D.G. Dorrell
Keyword(s):  
Line Bundle ◽  
Power Line ◽  
Lagrange Formalism

scholarly journals Gravity field recovery from orbit information using the Lagrange formalism

2017 ◽  
Vol 60 (3) ◽  
Author(s):  
Mohammad Ali Sharifi ◽  
Mohammad Reza Seif ◽  
Oliver Baur ◽  
Nico Sneeuw
Keyword(s):  
Gravity Field ◽  
Gravity Field Recovery ◽  
Lagrange Formalism

Lyapunov-stable control of mechatronic systems

2005 ◽  
Vol 219 (2) ◽  
pp. 173-185 ◽  
Author(s):  
O Enge ◽  
P Maißer
Keyword(s):  
Inverse Dynamics ◽  
Dynamic Control ◽  
Linear Feedback ◽  
Mechatronic Systems ◽  
Electromechanical Systems ◽  
Starting Point ◽  
Reaction Forces ◽  
The Stability ◽  
Lagrange Formalism ◽  
Stable Control

In this paper, a method for controlling mechatronic systems using inverse dynamics is proposed. The starting point is a unified mathematical approach to modelling electromechanical systems based on Lagrange formalism. This mathematical theory is used to represent such systems taking into account all interactions between their substructures. The concept of Lagrange formalism for electromechanical systems is given and the complete governing equations are presented. The Voronetz equations of a partially kinematically controlled electromechanical system (EMS) are derived. The corresponding reaction forces and voltages following from the Voronetz equations are determined. Using these reactions with small modifications, a so-called ‘augmented proportional-derivative (PD) dynamic control law’ is generated. This controller consists of a non-linear feedforward - based on inverse dynamics - and a linear feedback. The stability of the controller is proved using a Lyapunov function. The controller can also be applied to pure multibody systems or a sheer electrical system, both of which are borderline cases of mechatronic systems.

scholarly journals FRACTIONAL-ORDER PASSIVITY-BASED ADAPTIVE CONTROLLER FOR A ROBOT MANIPULATOR TYPE SCARA

Fractals ◽  
2020 ◽  
Vol 28 (08) ◽  
pp. 2040008
Author(s):  
J. E. LAVÍN-DELGADO ◽  
S. CHÁVEZ-VÁZQUEZ ◽  
J. F. GÓMEZ-AGUILAR ◽  
G. DELGADO-REYES ◽  
M. A. RUÍZ-JAIMES
Keyword(s):  
Fractional Order ◽  
Control Strategy ◽  
Control Method ◽  
Robot Manipulator ◽  
Adaptive Controller ◽  
Performance Comparison ◽  
External Disturbances ◽  
Scara Robot ◽  
Comparison Results ◽  
Lagrange Formalism

In this paper, a novel fractional-order control strategy for the SCARA robot is developed. The proposed control is composed of [Formula: see text] and a fractional-order passivity-based adaptive controller, based on the Caputo–Fabrizio and Atangana–Baleanu derivatives, respectively; both controls are robust to external disturbances and change in the desired trajectory and effectively enhance the performance of robot manipulator. The fractional-order dynamic model of the robot manipulator is obtained by using the Euler–Lagrange formalism, as well as the model of the induction motors which are the actuators that drive their joints. Through simulations results, the effectiveness and robustness of the proposed control strategy have been demonstrated. The performance of the fractional-order proposed control method is compared with its integer-order counterpart, composed of the PI controller and the conventional passivity-based adaptive controller, reported in the literature. The performance comparison results demonstrate the superiority and effectiveness of the fractional-order proposed control strategy for a SCARA robot manipulator.

Lagrange formalism in field theory

2021 ◽  
pp. 31-41
Author(s):  
Iosif L. Buchbinder ◽  
Ilya L. Shapiro
Keyword(s):  
Field Theory ◽  
Classical Field Theory ◽  
Momentum Tensor ◽  
Subsequent Treatment ◽  
Classical Field ◽  
Least Action Principle ◽  
Least Action ◽  
Field System ◽  
The Least Action Principle ◽  
Lagrange Formalism

This chapter is devoted to a general discussion of classical field theory. It presents the minimum information required about classical fields for the subsequent treatment of quantum theory in the rest of the book. The Lagrange formalism for the fields is introduced, based on the least action principle. Global symmetries are described, and the proof of Noether's theorem given. In addition, the energy-momentum tensor for a field system is constructed as an example.

Hamilton-Lagrange formalism of nonequilibrium thermodynamics

1994 ◽  
Vol 50 (2) ◽  
pp. 1227-1231 ◽  
Author(s):  
Katalin Gambár ◽  
Ferenc Márkus
Keyword(s):  
Nonequilibrium Thermodynamics ◽  
Lagrange Formalism
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